Give me a example of dividing polynomial by a binomial
Answer (1)
Answer:Here's an example of dividing a polynomial by a binomial using polynomial long division: Problem: Divide (x^2 + 5x + 6) by (x + 2). Solution: 1. Set up the long division: ___________x + 2 | x^2 + 5x + 6 2. Divide the first term of the dividend by the first term of the divisor:- x^2 / x = x. Write x above the 5x term. x _________x + 2 | x^2 + 5x + 6 3. Multiply the divisor by the term you just wrote down:- x * (x + 2) = x^2 + 2x. Write this below the dividend, aligning like terms. x _________x + 2 | x^2 + 5x + 6 x^2 + 2x 4. Subtract:- (x^2 + 5x) - (x^2 + 2x) = 3x. Bring down the +6 from the dividend. x _________x + 2 | x^2 + 5x + 6 x^2 + 2x -------- 3x + 6 5. Repeat the process:- Divide the first term of the new dividend (3x) by the first term of the divisor (x): 3x / x = 3. Write +3 next to the x above. x + 3 ______x + 2 | x^2 + 5x + 6 x^2 + 2x -------- 3x + 6 6. Multiply the divisor by the new term:- 3 * (x + 2) = 3x + 6. Write this below the 3x + 6. x + 3 ______x + 2 | x^2 + 5x + 6 x^2 + 2x -------- 3x + 6 3x + 6 7. Subtract:- (3x + 6) - (3x + 6) = 0. x + 3 ______x + 2 | x^2 + 5x + 6 x^2 + 2x -------- 3x + 6 3x + 6 -------- 0 8. Result: Since the remainder is 0, the division is exact. Answer: (x^2 + 5x + 6) / (x + 2) = x + 3
